PHY138 – Waves, Lecture 5 Today’s overview

1. PHY138 – Waves, Lecture 5Today’s overview • The Principle of Superposition • Standing Waves • The Guitar: Stringed Instruments • The Trumpet: Wind Instruments

2. Doppler Effect, Section 20.7 • When the observer is stationary, and the source is moving at speed vs directly toward or away from the observer: • When the source is stationary, and the observer is moving at speed vo directly toward or away from the source:

3. Which statement is true? Adrienne is standing in the middle of the road, as a police car approaches her at a constant speed, v. The siren on the police car emits a “rest frequency” of f0. • The frequency she hears rises steadily as the police car gets closer and closer. • The frequency she hears steadily decreases as the police car gets closer and closer. • The frequency she hears does not change as the police car gets closer.

4. Which statement is true? Adrienne is standing still as a police car approaches her at a constant speed, v. Suzanne is in her cadillac moving at the same constant speed, v, toward an identical police car which is standing still. Both hear a siren. Actual Answer! Check eq.20.38 and 20.39! • The frequency Suzanne hears is lower than the frequency Valerie hears. • The frequency Suzanne hears is higher than the frequency Adrienne hears. • The frequencies that Suzanne and Adrienne hear are exactly the same. (Almost correct)

5. Message from Dr. Savaria…. • If you have a conflict at 6:00-7:30 PM on Dec.4 and wish to write Test 2 at an alternate time: • Send an email to phy138y@physics.utoronto.ca (or reply to seeley) confirming that you wish to re-register, if you registered for the alternate sitting of Test 1. or • Visit April Seeley in MP129 or MP302 to register for the first time you will write in an alternate time. • The deadline for confirming / registering is Nov.26 by 5:00PM.

6. Reading Assignment • This week’s reading assignment from the text by Knight is: Chapter 21, Sections 21.1-21.8 • Suggested Chapter 21 Exercises and Problems for Practice: 7, 19, 25, 31, 49, 65, 71, 83 (skip part b – just use result) • Waves Quarter Written Team Problem Set is due Friday by 5:00 PM in T.A. drop box. – You must work in the teams assigned to you in tutorial.

7. Chapter 21: Principle of Superposition • If two or more waves combine at a given point, the resulting disturbance is the sum of the disturbances of the individual waves. • Two traveling waves can pass through each other without being destroyed or even altered!

8. Some Results of Superposition: • 21.2-21.4: Two waves, same wavelength and frequency, opposite direction: Standing Wave • 21.5-21.7: Two waves, same wavelength and frequency, similar direction, different phase: Interference • 21.8: Two waves, same direction, slightly different frequency and wavelength: Beats!

9. Standing Wave: The superposition of two 1-D sinusoidal waves traveling in opposite directions.

10. Standing Waves • Are a form of “resonance” • There are multiple resonant frequencies called harmonics • The boundary conditions and speed of waves determine which frequencies are allowed. • The ends of the resonant cavity have forced nodes or antinodes • With a wave on a string, it is possible to force an intermediate node

11. OMGWTFBBQ Standing Wave in Pressure Forces the Flames higher at antinodes!

12. Harmonic frequencies on a violin Transverse standing wave on a string clamped at both ends: there are nodes in displacement at both ends. A violin and all other stringed instruments almost always operate in the m = 1 or fundamental frequency.

13. Violin Demonstration A-string, fundamental frequency (A-note) A-string, second harmonic (m = 2, A-note) Higher octave A-note played in the normal way

14. Violin Demonstration A-string, third harmonic (m = 3, D-note) D-note played in the normal way Harmonic notes in sheet music: boxes

15. Harmonic frequencies in air column Standing sound wave in a tube open at both ends: there are nodes in pressure both ends. Standing sound wave in a tube closed at one end: there is a node in pressure at the open end, and an anti-node at the closed end.

16. Standing Wave Quiz The white wave is the sum of the blue and red waves. It is the A. Fundamental Frequency (m=1) B. Second Harmonic (m=2) C. Third Harmonic (m=3) D. Fourth Harmonic (m=4) E. Fifth Harmonic (m=5)

17. a Quiz b • A string is clamped at both ends and plucked so creates a standing wave. Define upward motion to be positive velocities. When the string is in position a, the instantaneous velocity of points along the string • A. is zero everywhere • B. is positive everywhere • C. is negative everywhere • D. depends on location

18. a Quiz b • A string is clamped at both ends and plucked so creates a standing wave. Define upward motion to be positive velocities. When the string is in position b, the instantaneous velocity of points along the string • A. is zero everywhere • B. is positive everywhere • C. is negative everywhere • D. depends on location c

19. a Quiz b • A string is clamped at both ends and plucked so creates a standing wave. Define upward motion to be positive velocities. When the string is in position c, the instantaneous velocity of points along the string • A. is zero everywhere • B. is positive everywhere • C. is negative everywhere • D. depends on location c

20. a Quiz b • A string is clamped at both ends and plucked so creates a standing wave. Define upward motion to be positive velocities. When the string is in position b, the instantaneous acceleration of points along the string • A. is zero everywhere • B. is positive everywhere • C. is negative everywhere • D. depends on location c